Federal Reserve Bank of Dallas Globalization and Monetary Policy Institute

Working Paper No. 292 https://dallasfedcm.ws.frb.org/-/media/Documents/institute/wpapers/2016/0292.pdf

Does Bitcoin Reveal New Information About Exchange Rates and Financial Integration?*

G. C. PietersTrinity University

December 2016

Abstract I show that the prices of the internationally traded crypto-currency bitcoin can be used to estimate a currency’s unofficial exchange rate and capital controls at a daily interval. Two important bitcoin features are documented: (1) Bitcoin-based exchange rates approximate the behavior, but not the level, of unofficial exchange rates, and (2) Bitcoin prices contain a bitcoin-trend term and must be appropriately normalized prior to being used for this purpose. Bitcoin-based exchange rates reveal that (3) there is no consistent pattern of Granger causality between unofficial rates and official rates by exchange rate regime or barriers at the daily frequency, and (4) that countries can engage in short-interval capital controls.

JEL codes: F31, F33, G15, O17

* Gina Pieters, Trinity University, Economics Department, 1 Trinity Place, San Antonio, TX 78212.gpieters@trinity.edu. I am grateful for helpful comments and suggestions from participants at the Fall2015 CSWEP meeting, the 2015 Southern Economic Association Conference, and the 2016 InternationalTrade and Finance Association Conference. The views in this paper are those of the author and do notnecessarily reflect the views of the Federal Reserve Bank of Dallas or the Federal Reserve System.

1 INTRODUCTION

It is difficult to obtain accurate data for unofficial exchange rates.1 Most papers examining unof-

ficial exchange rate behavior rely on the same data source: the World Currency Yearbook.2 Rates

in the World Currency Yearbook “are provided by the Central Bank and Ministries of Finance who

may be reluctant to provide the true data”, or reported by “foreign correspondents or informed

currency dealers”. [Bahmani-Oskoee, Miteza, and Nasir [2002]]. This data consists of a single

observation per month. Similar issues exist in attempting to quantify barriers to international fi-

nancial flows, as countries may impose unofficial barriers or put in place official barriers that have

no effect. Efforts to directly measure barriers, without relying on government reports, requires data

that is usually released only annually, limiting the frequency at which the barriers estimates can be

updated.3

Its virtual, online nature allows bitcoin to function both as a method to bypass restrictions on

the acquisition of foreign currency and as an alternative to the official, potentially manipulated,

exchange rate. I examine whether daily price data from bitcoin sales in various currencies can

be used to both construct a meaningful alternative dataset of daily unofficial exchange rates, and

be used to detect barriers to global financial integration.4 Because bitcoin prices can be directly

observed, this method requires no reporting agents, thereby removing potential reporting bias.

Moreover, because bitcoin has an alternative use as an investment vehicle, bitcoin trades exist even

if a currency is freely floating and therefore a bitcoin exchange rate for exists for currencies that

are both floating and managed.5

1I use to the term “unofficial” to broadly include what others call the market, black market, parallel, or de-factoexchange rates.

2The World Currency Yearbook was formerly known as Pick’s Currency Yearbook. Some papers cite Reinhartand Rogoff [2004] as their data source—this dataset was also built using the World Currency Yearbook. Papers thatdo not use the World Currency Yearbook are usually restricted to examining only one currency: for example, whileHuett, Krapf, and Uysal [2014] use online data, the trades are only for the Belarusian ruble to the US dollar, euro, andRussian ruble.

3Literature that estimates international financial barriers is reviewed in Section 4.3.4Minute-by-minute data is also available. However, to maintain a large sample size and reduce missing observa-

tions, daily data is used.5For example, Huett, Krapf, and Uysal [2014] found that trading of the Belarusin ruble ceased once the currency

was allowed to float.

2

The paper proceeds as follows. In Section 2 I provide a brief introduction to bitcoin, its history,

and relevant terminology and literature. In Section 3 I discuss data collection and bitcoin exchange

rate construction, and why the ratio of bitcoin prices does not trivially yield a usable exchange rate.

In Section 4, I use a cointegration test (either the Johansen trace test or the Pesaran-Shin-Smith

bounds testing procedure) and the results of a vector error correction model or conditional error

correction model to identify barriers to the acquisition of foreign currency. I identify exchange rate

manipulation by the magnitude of the bitcoin and official exchange rate ratio in Section 5. After

showing that bitcoin reflects the trend (but not the level) of unofficial exchange rates in section 6.1,

I update results in the literature regarding the relationship between official and unofficial exchange

rates—previously focused on managed exchange rate regimes and using monthly observations—

for the remainder of Section 6. Specifically, I show that (1) the proportionality restriction (required

for many models of unofficial market exchange rates) exists for all exchange rate regimes as long

as there are no restrictions to access of foreign currency; and (2) Granger causality between the

official and bitcoin exchange rate follows no consistent pattern across regimes or barriers when

using daily exchange rate data.

2 WHAT IS BITCOIN? A BRIEF HISTORY

The purpose of this section is to give the interested reader only as much information as needed to

understand bitcoin for this paper. For a comprehensive overview of bitcoin, readers should consult

Velde [2013]. Bohme, Christin, Edelman, and Moore [2015] wrote an accesible technical review of

bitcoin, and Brandvold, Molnar, Vagstad, and Valstad [2015] contains a brief discussion of major

events in bitcoin history. White [2015] considers the market for crypto-currencies more broadly.

Bitcoin is a crypto-currency designed and created by the entity Nakamoto [2008].6 A crypto-

currency is entirely digital, with no central monetary authority, country of origin, or physical rep-

resentation. Nakamoto created 21 million bitcoin, which are discovered by solving mathematical

algorithms in a process known as “mining”. Once discovered, a bitcoin can be held, used for retail

6The name Satoshi Nakamoto is a pseudonym. The identity of Satoshi (person or persons) is currently unknown.

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purchases, or bought and sold on a bitcoin trading website in exchange for a variety of currencies.7

Dwyer [2015] explores why the ability to use bitcoin for these purposes could result in a crypto-

currency with a positive price, while Luther [2016] examines conditions under which a positive

price may not result even if bitcoin is superior to existing monies.

A website where bitcoin can be bought and sold is known as an “exchange.” Every account on

an exchange has a virtual “wallet” in which the users can store both their bitcoin8 and the curren-

cies accepted by the exchange. Currency in a wallet can be directly deposited into or withdrawn

from a connected bank account, an online payment system (such as PayPal), or into a wallet asso-

ciated with a different exchange. An example of an exchange buy/sell interface is shown in Figure

1, using the exchange ANXBTC. An exchange user can buy bitcoin using currency in their wallet

(in Figure 1, US dollars would be used to purchase bitcoin) and in a matter of seconds, sell the

purchased bitcoin for a different currency (selecting EUR from the drop-down menu would sell

the bitcoin for euros), which would be deposited back into their wallet. This illustrates why the

bitcoin price in US dollars and in euros can be used to construct an exchange rate: bitcoin can

function like a vehicle currency for foreign exchange swaps, a role traditionally held by the US

dollar.9 Unlike traditional vehicle currencies, access to bitcoin (and its associated exchange rate to

other foreign currencies) is very difficult to restrict as it requires preventing individuals from ac-

cessing any one of exchange websites.10 Additionally, bitcoin prices in different currencies among

various independent, globally established exchanges are publicly and instantaneously available to

all agents without charge regardless of the agent’s country of origin.

The online nature and pseudo-anonymity of bitcoin has resulted in its use in online criminal

transactions.11 The “Silk Road” market is the most widely known example. Silk Road was not

7I use the term “currency” to refer exclusively to a currency issued by a central monetary authority (e.g., the USdollar) as opposed to crypto-currencies, such as bitcoin or litecoin.

8Technically, the wallet does not actually “store a bitcoin,” though from a user’s perspective, this is functionallywhat occurs. For details, refer to Bohme, Christin, Edelman, and Moore [2015].

9Systems for direct currency trades have recently been implemented by some exchanges. As these systems are stillin their infancy (having poor data availability), transactions of this nature will not be considered.

10Hendrickson, Hogan, and Luther [2016] consider governmental efforts to discourage bitcoin use.11Contrary to popular belief, bitcoin is not anonymous. The entire transaction history of a bitcoin travels with it in

the bitcoin’s publicly visible “blockchain”—equivalent to a digital ledger. Pieters and Vivanco [2015] have examinedthe implication of this on bitcoin pricing, finding that it contributes to the bitcoin market segmentation that is also

4

FIGURE 1Buy/Sell Interface on the ANXBTC Bitcoin Exchange

a bitcoin exchange; rather, it was an online marketplace for the sale of drugs and other illegal

activities where transactions were conducted in bitcoin to reduce the ability of law enforcement to

trace payments. Bitcoin has a variety of legal uses as well—an investment asset, or as a means to

purchase goods from major companies (Dell and Amazon both allow the purchase of items using

bitcoin, either directly or through the purchase of a gift card). Because bitcoin has these other uses,

even currencies with unrestricted capital markets and unmanipulated exchange rates have bitcoin

trading activity, and therefore, a bitcoin price. These uses allow for the construction of a bitcoin

exchange rate for currencies with a variety of exchange rate regimes, from the euro and Canadian

dollar to the Chinese yuan and Argentinian peso.

A major structural change to the bitcoin market occurred after the sudden failure and bankruptcy

of Mt. Gox, an exchange that handled up to 80% of the world’s bitcoin trade, in February 2014.12

Given the enormity of the changes that followed the Mt. Gox collapse, this paper only focuses

detected in this paper.12CoinDesk (www.coindesk.com/companies/exchanges/mtgox) provides more details surrounding this event.

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on the period after June 1, 2014, when the bitcoin market stabilized after nearly six months of

instability and structural changes, even though the first bitcoin was traded in January 2009.13

3 EMPIRICAL APPROACH

3.1 DATA SOURCES

Bitcoin are bought and sold in many different currencies and exchanges (the aggregation website

Bitcoin Charts [bitcoincharts.com] provides data from 72 exchanges trading 31 currencies). To

create a comparable cross-country study, I will examine only exchanges that conduct transactions

in at least three different currencies, of which two must be the US dollar and the euro. I obtain

the daily transaction-weighted price from the Bitcoin Charts website, and include only currencies

that report at least 400 transactions during the period of the study: June 1, 2014, to September

30, 2015.14 This selection process yields an initial selection of 22 currencies traded across four

exchanges, ANXBTC, itBit, BTC-e, and LocalBitcoin. The currencies and exchanges studied in

this paper therefore only include a subset of all the transactions, and while some currencies appear

only once in my sample, all currencies studied trade on multiple bitcoin exchanges, most of which

are not included.

Table 1 lists current price observations, along with current restrictions on bitcoin trades appli-

cable to each currency’s country of origin during the period of study. Most countries in this sample

have no bitcoin trading laws; the those that do mostly only apply standard money-laundering or

counterterrorism laws, or ban financial firms or banks from trading bitcoin. Russia and Thailand

are the only two countries that appear to have banned bitcoin trades, yet statements by Russian

politicians have contradicted this position, and bitcoin-based businesses have received licenses in

Thailand. As neither of these countries can regulate bitcoin trades that occur in their currency

13An early study of bitcoin price behavior by Yermack [2015] concluded that the bitcoin daily exchange rate exhib-ited nearly zero correlation with major currencies. This conclusion was based on an examination of correlations usingMt. Gox prices from July 17, 2010, to the day prior to its collapse (February 6, 2014). Even without the Mt. Goxcollapse, this date range includes several dramatic events in bitcoin price history not discussed here that could biasresults.

14Because bitcoin exchanges do not close for trading, each trading day is defined as starting at midnight CoordinatedUniversal Time (UTC) regardless of the location or currency traded on the exchange.

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TABLE 1Summary of Bitcoin Price, Volume, and Legal Status Across Exchanges and Currencies

Exchange Average Daily Volume AverageSymbol Currency Obs. BTC Currency Price Bitcoin Trade Legal Status

ANXBTC (https://anxbtc.com)USD US dollar 480 910.88 319,185.72 344.56EUR Euro 480 908.86 259,909.33 282.12AUD Australian dollar 480 908.12 377,217.71 409.85CAD Canadian dollar 480 907.85 370,268.77 401.73 AML and CTCHF Swiss franc 418 12.93 3,862.03 345.10 AMLCNY Chinese yuan 480 907.91 1,974,068.91 2,134.54 Financial firms forbiddenGBP British pound 480 907.59 198,726.70 215.60HKD Hong Kong dollar 480 908.76 2,472,351.55 2,671.54 AML and AFJPY Japanese yen 480 907.53 35,591,785.03 38,765.43NZD New Zealand dollar 480 907.92 408,896.33 445.12 Banks need approvalSGD Singapore dollar 480 907.57 414,722.76 449.60

BTC-e (https://btc-e.com)USD US dollar 476 7,554.94 2,355,088.31 341.53EUR Euro 481 114.40 32,250.93 284.17RUB Russian ruble 480 309.06 4,878,341.97 16,861.43 Unclear; appears to be illegal

itBit (https://www.itbit.com)USD US dollar 487 2,787.36 819,134.79 344.76EUR Euro 476 351.50 80,574.17 280.17SGD Singapore dollar 484 236.83 88,561.27 448.39

LocalBitcoins (https://localbitcoins.com)USD US dollar 487 1,705.08 552,005.11 382.89EUR Euro 487 209.19 54,929.90 292.98ARS Argentinian peso 448 13.46 51,044.50 4,400.49AUD Australian dollar 487 199.80 78,206.06 430.62BRL Brazilian real 434 5.76 5,218.54 985.43CAD Canadian dollar 487 47.15 17,598.88 418.46 AML and CTCHF Swiss franc 418 12.93 3,862.03 345.10 AMLCZK Czech Republic koruna 401 2.91 20,330.17 7,871.56GBP British pound 487 518.40 105,941.87 222.64INR Indian rupee 487 17.72 322,911.44 21,748.92MXN Mexican peso 487 15.31 71,072.77 5,127.63 AML and AFNOK Norwegian krone 474 11.17 25,563.80 2,510.87NZD New Zealand dollar 485 10.37 4,596.90 462.47 Banks need approvalPLN Polish zloty 468 8.25 8,529.66 1,151.59RUB Russian ruble 487 148.26 2,298,994.40 17,007.64 Unclear, appears to be illegalSEK Swedish krona 487 43.51 102,627.89 2,747.46SGD Singapore dollar 442 3.92 1551.87 478.31THB Thai bhat 487 35.42 368.493.30 11,177.79 Officially illegalZAR South African rand 487 51.97 193,764.97 4,293.01Abbreviations: AF, anti-fraud laws; AML, anti-money laundering; (blank), unrestricted trade; BTC, units of bitcoin;

CT, counterterrorism laws; Obs., observations.

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outside of their borders (for example, someone in Canada buying bitcoins with Russian Rubles), I

assume the impact that these regulations have on the global bitcoin market is minimal.

The average daily volume of trade measures the bitcoin trades conducted in the indicated cur-

rency, either in units of bitcoin (BTC) or in the currency indicated. The volume of trades measured

in bitcoin is slightly misleading because a bitcoin is highly divisible: the smallest bitcoin unit is the

bitcoin-satoshi, which equals 10−9 bitcoin (a hundred-millionth of a bitcoin). US dollar trades are

the most popular trades (as measured by BTC) for all exchanges in this sample. While trade vol-

umes on bitcoin markets represent only a small fraction of the official currency markets, even the

smallest exchange has a daily volume of over a quarter-million US dollars in USD-bitcoin trades.

Official exchange rate data come from Oanda.com. Oanda reports the average exchange rate

over a 24-hour period of global trading, seven days a week—a structure similar to the exchange

rate created by bitcoin data. I linearly interpolate each series to estimate missing values, resulting

in 487 daily observations per bitcoin exchange and currency.

3.2 DEFINING BITCOIN EXCHANGE RATES

Using bitcoin prices in the currency of interest (BCm,t) and the US dollar (BUSD

m,t ) the implied bitcoin

exchange rate, (EB,Cm,t ), is given by:

EB,Cm,t = BC

m,t/BUSDm,t (1)

for exchange (m) on day (t) between currency (C) and the US dollar. This equation uses bitcoin

as a vehicle currency, buying bitcoin in one currency to sell it for another.

Figure 2 shows the bitcoin US dollar to Euro exchange rate constructed for the four selected

exchanges, as well as the official exchange rate. The bitcoin exchange rate constructed from

ANXBTC and itBit data almost indistinguishable from the official exchange rate, unlike the ex-

change rate calculated using BTC-E and LocalBitcoins data. As the USD-Euro exchange rate

represents the most easily accessible official and bitcoin exchange rates across the various curren-

cies, this figure shows why the question of how to appropriately compare bitcoin exchange rate to

official exchange rate data is even asked, as the data from various exchanges do not appear to be

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FIGURE 2USD to Euro Exchange Rate for Four Exchanges

interchangeable. This is consistent with the findings of Pieters and Vivanco [2015], who show that

arbitrage is not satisfied across the various bitcoin exchanges due to differences in the structure of

the exchanges.

I assume the relationship between bitcoin and official exchange rates across the various ex-

change markets consists of two terms: a stationary, potentially non-zero, mark-up term, (εC,m),

and a trend difference term, (ρC,m), and can be expressed in the form15:

EB,Cm,t =

(1+ρC,m

)EO,C

t + εC,m (2)

The absolute Law of One Price (aLOP) requires that the bitcoin and official exchange rates are

identical, ρc,m = 0 and εC,m = 0, while relative Law of One Price (rLOP) allows for a level differ-

ences and requires only that the two exchange rates follow the same trend, ρc,m = 0 and εC,m 6= 0.

A failure of the absolute law of one price is expected because both the bitcoin exchanges and

official currency vendors charge fees for currency trades, thereby introducing an arbitrage band,

εC,m 6= 0, into the markets. This band can be identified in Figure 2 as the non-zero difference be-

15I refer to ρC,m as a trend difference term as it captures the differences in the trend of the two series: EB,Cm,t −EB,C

m,t−1 =

(1+ρc,m)(

EO,Ct −EO,C

t−1

)

9

tween the official and bitcoin exchange rates. The trend difference, ρc,m, is most easily be seen as

the increasing distance between LocalBitcoin and the official exchange rate series (recall that εC,m

is stationary).

Akram, Rime, and Sarno [2008] studied global financial and exchange rate contracts of dif-

ferent durations, and found that most price deviations in exchange rate markets were quickly arbi-

traged away, implying that exchange rates across foreign exchange markets should adhere to rLOP.

Relative to official exchange rate markets, the bitcoin’s global simultaneity (exchanges never close)

and ease of comparison of prices across bitcoin markets (bitcoin prices in all currencies are globally

and simultaneously available to the public at no charge, and there are no exchange rate contracts of

different lengths) imply that arbitrage opportunities caused by the difference between the official

and unofficial exchange rates should be found and exploited by any participant even more quickly

and easily than on the official markets studied in Akram, Rime, and Sarno [2008]. However, Yer-

mack [2015] argues that bitcoin should not be thought of as a currency and should, therefore, be

treated as a traded good. In examining the behavior of car prices across the eurozone after the

introduction of the euro, Goldberg and Verboven [2005] found convergence to both the absolute

and relative law of one price, while in a study examining consumer goods prices across European

cities, Engel and Rogers [2004] found no evidence of convergence. It is therefore possible that

some aspect of bitcoin or a bitcoin exchange—one that cannot be easily removed—could over-

whelm convergence to the exchange rate causing rLOP between the official and bitcoin exchange

rate to fail.

I assume that the trend difference term, ρc,m, can be decomposed into three components:

ρC,m = ρB +ρ

m +ρC (3)

The deviation from the official exchange rate trend that occurs because of bitcoin—and is therefore

shared across all bitcoin exchanges and currencies—is reflected in (ρB). The bitcoin-exchange-

specific wedge—capturing differences in fees or structures specific to a bitcoin exchange—is re-

10

flected in (ρm). Finally, (ρC) denotes any deviations between the official and bitcoin exchange

rates that are currency-specific.16 All components can take positive or negative values. Given

an estimate of ρC,m for two different currencies, C1 and C2, on the same exchange m, the form

assumed in Equation (3) allows a normalized currency-specific wedge to isolated, removing the

impact of both bitcoin and the exchange:

ρC1,m−ρC2,m = ρC1−ρ

C2 ≡ ρC1,C2 (4)

Studying the prices of stocks that trade on both domestic and international markets, Yeyati,

Schmukler, and Horen [2009] showed that price segmentation resulted from cross-border capital

regulations functioning as a barrier in international financial markets. Similarly, Goldberg and Ver-

boven [2005] interpreted the reduction in car price segmentation across the eurozone as a reduction

in the barriers in the international goods market. Therefore, irrespective of whether bitcoin should

be thought of as a good or as money, ρC1,C2 6= 0 can be interpreted as implying the existence of

a barrier in accessing official exchange rates from the bitcoin exchange rate market, while a find-

ing of ρC1,C2 = 0 is consistent with rLOP in exchange rates. After describing the method used to

estimate ρC1,C2 in Section 3.3, I shall verify in Section 4.3 that estimates of ρC1,C2 reflect known

barriers in the currency market, verifying that the bitcoin components are removed from ρC1,C2 in

this normalization, as part of the contribution of this paper.

3.3 TESTING FOR COINTEGRATION

As both the official and bitcoin exchange rate series for each currency are found to be nonstationary,

determining whether ρC1,C2 = 0 requires care. First I test the official and bitcoin exchange rates for

cointegration. A failure to find cointegration is inconsistent with flexible, market-based exchange

rates because it implies that the official and bitcoin exchange rates do not share a trend. This

failure is consistent with a barrier in access to international exchange markets (for example, capital

16Technically, equation 3 can be generalized, as all that is needed is for the currency component to be seperable.

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controls or a lack of market access).17

I use either the Johansen trace test or the Pesaran-Shin-Smith (PSS) bounds testing proce-

dure. The Johansen trace test is the default method to determine cointegration, however it requires

that the series tested be integrated to the same order and be I[1] (also referred to as unit root,

first-difference stationary, or having order of integration one). This requirement is not met by all

exchange rates in this sample because some are fractionally integrated (between I[0] and I[1]),

or one series of the pair is fractionally integrated, while the other is I[1]. Because the fractional

integration of a series could be the result of the exchange rate regime or barriers to access, these

series are not simply removed. The PSS bounds test allows for both fractional integration and for

the two series to have different orders of integration, but it is more restrictive in that it requires the

series to display a single direction of causality.

3.3.1 Order of Integration I test the order of integration of each exchange rate series at a given

lag using tests with opposing nulls for robustness: an augmented Dickey-Fuller test [ADF; Dickey

and Fuller, 1979], which has a null of the series being I[1], and a Kwiatkowski-Phillips-Schmidt-

Shin [KPSS; Kwiatkowski et al., 1992] test, which has a null of the series being I[0] (stationary or

having order of integration zero). A series that is truly I[1] should both accept the ADF test and

reject the KPSS test.

If both the official and bitcoin exchange rate series for a given currency accept ADF and reject

KPSS, the requirements of the Johansen trace test are satisfied. Series that accept both ADF and

KPSS could be either fractionally integrated or integrated to an order higher than I[1]. To differ-

entiate, I re-run the ADF and KPSS tests on the first difference of the series. I consistently find

that the first difference rejects ADF and accepts KPSS; therefore, the original series is fractionally

integrated and the methods of the PSS bounds test are applied to that currency instead.

17Cointegration tests are biased against finding cointegration if one of the series contains a structural break. Withinthis setting, however, the exchange rate series should share the timing and magnitude of a structural break if there areno barriers, so a finding of no cointegration in this setting is consistent with the interpretation of a barrier. Therefore,I do not include controls for structural breaks.

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3.3.2 Johansen Trace Test. The Johansen test iteratively tests a null hypothesis that no more than

r equations exist, which describe the trend relationship between n series (with r = 0 indicating no

cointegration), accepting the first value of r for which the null is not rejected. As I consider only

two series, there can be at most one cointegrating equation, so the test should obtain significant

results for r = 1 if the two sources of exchange rates are to be cointegrated.

The trace test is based on a vector error correction model (VECM). Given the vector of the

bitcoin and official exchange rate for a given market and currency, ECm,t = [EB,C

t ,EO,Cm,t ] (where

market and currency notations are suppressed in future equations for clarity), the VECM estimates

the following:

∆Et =`

∑i=1

Γi∆Et−i + γΠ′Et−1 +α + εt (5)

where ∆Et = Et −Et−1, ` is the lag, and εt are standard mean zero, independent, identically dis-

tributed shocks. I select the initial lag according to the Schwarz Bayesian information criterion

(SBIC).

After running the VECM at lag `, a Lagrangian multiplier (LM) test is used to test for auto-

correlation in the residuals. If the LM test null of no autocorrelation is rejected at the 5% level,

the value of the lag is incremented by one. The order of integration and the tests for residual

autocorrelation are repeated. If the null is not rejected, the Johansen trace test is applied.

The cointegrating relationship between the two series is captured in Π, where Π = [1,−β ].

Among cointegrated series, β is the variable of interest because a failure to find β = 1 implies that

the bitcoin exchange rate growth (the long-run trend) is either larger (β > 1) or smaller (β < 1)

than the official exchange rate.

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3.3.3 PSS Bounds Test The PSS bounds test is based on the unrestricted conditional error-

correction model (CECM), expressed in notation from Section 3.3.2 as:

∆Eyt = α +

`

∑i=1

Γi∆Et−i + γΠ′ logEt−1 +ω

′∆Ex

t + εt (6)

where y refers to either the bitcoin or official exchange rate, and x refers to the exchange rate not

used in y, and ` is the lag (initially selected by SBIC or passed by the process in Section 3.3.2).

A significant restriction of the PSS method is that the CECM requires a single direction of

causality, which I establish before proceeding. In Equation (6), I assume that Ext causes Ey

t , or in

the parlance of PSS, Ext is the forcing function for Ey

t . Given the presence of series that are not

I(0), I use the methodology of Toda and Yamamoto [1995] (TY) to determine Granger causality,

first estimating a vector autoregression model (VAR) on the data with lags `+1:

Et = c+`+1

∑i=1

ΨiEt−i + εt (7)

where Et−(`+1) is an exogenous variable. If I find residual autocorrelation at either ` or `+1, the lag

is incremented and the procedure repeated, with each series order of integration once again verified.

If I find that both series are unit root processes, the Johansen trace test (described in Section 3.3.2)

is applied. Otherwise, causality is tested using the TY methodology described above.

If I establish a single direction of causality between the bitcoin and the official exchange rate

series, I can use the PSS bounds test. The PSS bounds test evaluates the joint significance of the

coefficients for lagged variables using a Wald test, comparing the resulting F-statistic to an upper

and lower bound calculated by Pesaran, Shin, and Smith [2001]. For this paper, the bounds for the

critical values (c.v.) are the following:

H0: No Cointegration 1% c.v. 5% c.v. 10% c.v.Accept H0 if F< c.v. 6.84 4.94 4.04Reject H0 if F> c.v. 7.84 5.73 4.78

If the F-statistic is lower (higher) than the lower (upper) critical bound, then the null hypothesis

14

of no cointegration is rejected (accepted) regardless of the underlying series order of integration.

If the F-statistic falls between the critical bounds, I must use information on the underlying series

order of integration.

4 BARRIERS TO ACCESSING FOREIGN CURRENCY

4.1 ADJUSTING FOR BITCOIN-SPECIFIC BARRIERS

I compare the behavior of the bitcoin and official exchange rate across the four bitcoin exchanges

for the euro in Table 2. The bitcoin exchange rate on LocalBitcoins is fractionally integrated, so I

use the PSS bounds test after determining that causality occurs from the official exchange rate to the

bitcoin exchange rate. I use the Johansen trace test for the other three exchanges. Across all four

bitcoin exchanges, the official and bitcoin exchange rates are cointegrated, as would be expected

for standard financial markets given an exchange rate with minimal restrictions on foreign currency

trades.

TABLE 2Euro-USD Cointegration Test

Lag Johansen Trace Test PSS Test Barrier SizeMarket SBIC ` r=0 r=1 F-stat C? β EUR,M ρEUR

ANXBTC 2 2 242.65 2.05∗∗∗ − Y 1.00∗∗∗ 0.00BTC-e 3 4 25.19 2.06∗∗∗ − Y 0.96∗∗∗ 0.00itBit 2 2 193.76 2.21∗∗∗ − Y 1.02∗∗∗ 0.00LocalBitcoins 2 4 − − 50.89∗∗∗ Y 0.74∗∗∗ 0.00***1%, ** 5%.Abbreviations: C, Cointegrated series

The VECM or CECM estimated trend coefficient of the cointegrating equation, β EUR,M re-

ported in Table 2, is more interesting as it is not true across all exchanges that β EUR,M = 1, even

though the Euro exchange rate is a major, easily accessible market. The relationship between

the estimated long-run cointegrating relationship, β EUR,M and the trend difference introduced in

Section 3.2 can be expressed as:

βEUR,M = 1+ρ

B +ρM +ρ

EUR (8)

15

The β EUR,ANX = 1 result of ANXBTC implies that the rLOP holds; the trend difference compo-

nent is calculated to be ρB +ρANXBTC +ρEUR = 0. As expected given Figure 2, this is not strictly

true for the remaining three exchanges, with LocalBitcoins exhibiting a substantial deviation. Ta-

ble 2 therefore verifies a significant result implied by the visual examination of Figure 2: while

it may be tempting to assume that the rLOP should hold between bitcoin and official exchange

rates trends, or that βC,M = 1 and(ρB +ρm +ρC) = 0, this may not be a valid assumption due

to non-negligible trends within either bitcoin or the bitcoin exchange. Therefore, I use β EUR,M to

normalize the remaining estimates and remove bitcoin-specific (ρB) and exchange-specific (ρM)

effects for any currency, using equation 4 to generate ρC1,C2 as defined in Section 3.2. This esti-

mates the currency trend wedge relative to the euro trend wedge (ρC), normalized to range from

zero to one:

ρC = ρ

C,EUR

||βC,M− β EUR,M||, if cointegrated

1 otherwise(9)

This value is reported in the final column of Table 2. The highest value of ρC = 1 indicates high

barriers to access official exchange rate markets, while the lowest value of ρC = 0 indicates a

barrier equivalent to that of the USD-EUR exchange rate (low barriers), while the effective size of

a country’s barrier can then be ranked based on its distance from ρC = 0.

4.2 DETECTING BARRIERS IN INTERNATIONAL FINANCIAL MARKETS

Assessing the extent of effective barriers to international currency flows is a difficult task, as re-

strictions may be mostly unofficial, or may only be occasionally binding. A standard measure of

barriers to international capital movement is the Chinn-Ito Financial Openness index (KAOPEN),

originally developed by Chinn and Ito [2006] and recently updated to 2013. The KAOPEN ranges

from zero (no barriers) to one (high barriers), and is constructed from the values of four annual bi-

nary dummy variables from the International Monetary Fund’s (IMF) Annual Report on Exchange

Arrangements and Exchange Restrictions. Specifically, it is based on four dummy variables that

indicate the presence of multiple exchange rates, restriction on current account transactions, restric-

16

tions on capital account transactions, or a requirement of the surrender of export proceeds. The

data underlying the KAOPEN ranking is therefore substantially different from the bitcoin-based

estimate of barriers, which is based on non-binary daily pricing data.

While KAOPEN will be used as the point of comparison to evaluate whether bitcoin-based

inferences can be considered accurate, it is not the only index that measures financial openness and

integration. Bekaert and Harvey [2005] constructed a binary index based on the date of financial

liberalization, while Lane and Milesi-Ferretti [2007] base their index upon measures of a country’s

exposure to international financial markets. The index constructed in a manner most similar to the

bitcoin index is based on stock price differences and constructed by Yeyati, Schmukler, and Horen

[2009].18 A comparison of the various indices can be found in Quinna, Schindler, and Toyoda

[2011].

4.3 DOES BITCOIN REVEAL BARRIERS TO OFFICIAL EXCHANGE RATE MARKETS?

Table 3 presents results from the cointegration tests, the unadjusted trend coefficients β , and es-

timated barrier ρC.19 I divide all results into three broad categories, and within each category

currencies are sorted by their lowest value of ρC. A “High Barriers” currency failed to find coin-

tegration, while both the “Low Barriers” and “Intermediate Barriers” currency obtained cointegra-

tion results (indicated by values of “N” and “Y” respectively under the column heading “C?”). For

currencies with cointegration results, there is the question of what value of ρC indicates a barrier

that, while not significant enough to completely decouple the two markets, is sufficient to indicate

a potential burden for users of official exchange rates of that currency. I use the results from CAD

and SGD, which report ρC results from two exchanges, as a guide to an appropriate interval. Low

barriers are defined as ρC in the interval [0.0,0.1], and intermediate barriers as ρC > 0.1. Note

that using the unadjusted coefficient, β , that does not remove bitcoin-specific trends would yield a

different ordering of barriers, illustrating the importance of adjusting for bitcoin-specific trends in

18Results are not compared to this index because it terminates in 2004.19The bitcoin exchange rate data from ANXBTC for HKD, and LocalBitcoins for AUD, CHF, GBP, HKD, INR,

NZD, RUB, and SGD, are problematic (either exhibiting residual autocorrelation, or failing to yield a single directionof causality); thus, they were removed.

17

the exchange rate market.

TABLE 3Existence and Size of Exchange Rate Barriers

Lag Johansen Trace Test PSS Test Barrier SizeCurrency Market SBIC ` r = 0 r = 1 F-stat C? β ρC KAOPEN

Low BarriersCAD ANX 1 1 1154.08 0.02∗∗∗ − Y 1.00∗∗∗ 0.00 0.00

Local 2 2 135.40 0.02∗∗∗ − Y 0.65∗∗∗ 0.09 0.00GBP ANX 1 1 1152.46 2.13∗∗∗ − Y 1.00∗∗∗ 0.00 0.00JPY ANX 2 2 213.77 2.63∗∗∗ − Y 1.00∗∗∗ 0.00 0.00NZD ANX 2 2 224.07 0.03∗∗∗ − Y 1.00∗∗∗ 0.00 0.00SGD ANX 2 2 231.27 0.01∗∗∗ − Y 1.00∗∗∗ 0.00 0.00

itBit 2 3 144.25 0.01∗∗∗ − Y 0.93∗∗∗ 0.09 0.00CZK Local 2 5 − − 32.84∗∗∗ Y 0.74∗∗∗ 0.00 0.00AUD ANX 1 1 1318.26 0.05∗∗∗ − Y 1.00∗∗∗ 0.00 0.19RUB BTC-e 2 2 31.91 1.23∗∗∗ Y 0.93∗∗∗ 0.03 0.29THB Local 2 2 − − 109.67∗∗∗ Y 0.77∗∗∗ 0.03 0.84BRL Local 1 4 67.18 4.04∗∗∗ − Y 0.81∗∗∗ 0.07 0.59SEK Local 2 2 − − 51.17∗∗∗ Y 0.81∗∗∗ 0.07 0.00

Intermediate BarriersPLN Local 2 3 − − 61.25∗∗∗ Y 0.86∗∗∗ 0.12 0.55CHF ANX 3 3 − − 67.03∗∗∗ Y 1.17∗∗∗ 0.17 0.00NOK Local 2 3 116.99 0.67∗∗∗ − Y 0.93∗∗∗ 0.19 0.00

High BarriersMXN Local 2 2 14.04∗∗∗ 0.08 − N − 1.00 0.31ZAR Local 2 6 15.13∗∗∗ 0.37 − N − 1.00 0.84CNY ANX 2 3 3.59∗∗∗ 0.38 − N − 1.00 0.84ARS Local 6 6 5.44∗∗∗ 0.79 − N − 1.00 1.00Abbreviations: ANX, ANXBTC; C, cointegrated series; KAOPEN, Chinn-Ito Financial Openness index;

Local, LocalBitcoin; PSS, Pesaran-Shin-Smith; SBIC, Schwarz Bayesian information criterion.***1%, ** 5%.

With seven exceptions, the barriers of each of the currencies are in the same order as presented

in KAOPEN. Four are found to have lower barriers relative to other countries than those reported

by KAOPEN, and three have higher barriers than reported by KAOPEN. I examine the reasons for

these seven deviations in Sections 4.3.1–4.3.3, and find them to reflect either the granularity of the

data, or the newer nature of the bitcoin data. I therefore conclude that an alternative measure of

barriers can be constructed using bitcoin data.

18

FIGURE 3Comparison of Unadjusted Bitcoin and Official Exchange Rates: Minimal Barriers

(a) Canadian Dollar (b) British Pound (c) Japanese Yen

(d) New Zealand Dollar(e) Singapore Dollar

(f) Czech Rep. Koruna

(g) Australian Dollar (h) Russian Ruble (i) Thai Bhat

(j) Brazilian Real (k) Swedish Krona

4.3.1 Low Barrier Currencies Among the 11 countries that bitcoin reports to have low barriers,

four deviate from their KAOPEN ranking: Australia (AUD, Figure 3[g]), Russia (RUB, Figure

19

FIGURE 4Comparison of Unadjusted Bitcoin and Official Exchange Rates: Intermediate Barriers

(a) Polish Zloty (b) Swiss Franc (c) Norwegian Krone

3[h]), Thailand (THB, Figure 3[i]), and Brazil (BRL, Figure 3[j]).

Recall that the bitcoin data I use for this study are based on 2014 and 2015 information, while

KAOPEN is based on 2013 data. KAOPEN documents a trend of decreased barriers in both Aus-

tralia (since 2011) and Russia (since 2008). It therefore seems likely that finding of lower barriers

using bitcoin than the KAOPEN results from a continuation of this trend.

While I do not find evidence of barriers the remaining two countries, Thailand and Brazil, in

section 5.2 I show that they appear to have managed exchange rates based upon the magnitude

of the difference between the offical and bitcoin exchange rates, consistent with the findings of

KAOPEN. The bitcoin-based results of Table 3 imply that during the period of this study, these

two countries (which have managed exchange rate regimes in KAOPEN) did not maintain their

exchange rate regimes by limiting access to foreign currency, but may instead use policies such as

interest rate manipulation or monetary policy.

4.3.2 Intermediate Barrier Currencies Among currencies with intermediate barriers, both the

Swiss franc (CHF) (Figure 4[b]), and the Norwegian krone (Figure 4[c]) are found by bitcoin

to be more restricted than KAOPEN reports.

Prior to January 15, 2015, the Swiss National Bank (SNB) had a minimum exchange rate peg

in place relative to the euro. Comparing the official and bitcoin exchange rates in Figure 4[b],

it appears this peg had been binding as the two exchange rates do not share a similar trend. On

20

January 15, the SNB formally abandoned its peg (to the apparent surprise of all market participants

given the reaction in both markets) and lowered its target interest rate further into negative terri-

tory.20 After the removal of the peg, bitcoin and official exchange rates appear to share a trend.

While the peg had been in place since September 2011 and is therefore in the data used to con-

struct KAOPEN, it may not have been a binding minimum constraint during that time. For the

Norwegian krone (NOK), a structural break in the bitcoin exchange was detected on December

8, 2014. Unlike the Swiss franc, no obvious event coincides with this date. However, given that

Norway is physically proximate to eurozone countries that underwent great economic upheaval

during this time period, it is possible that the NOK exchange rate anomaly reflects spillover from

those economies.

4.3.3 High Barrier Currencies Of the four countries that have high barriers, Mexico (Figure

5[a]) is found to have more capital restrictions than expected given KAOPEN. While Mexico is

commonly classified as a freely floating exchange rate, it strongly rejects cointegration with the

bitcoin exchange rate. Though several factors could explain a change in the exchange rate (the

fall of oil prices; implementation of austerity cuts; a political scandal), none of these events can

explain a divergence between the official and bitcoin exchange rates visible at the beginning of Oc-

tober 2014. The last paragraph on page 53 of the Banco de Mexico January–March 2015 Quarterly

Report [Banco De Mexico, 2015], detailed in more depth by Cardenas [2015], briefly mentions a

possible cause. Informally, Mexico has an acceptable band for its exchange rate. The exchange

rate moved out of this band, causing the central bank to intervene and manipulate its exchange rate

through an auction. This intervention—which represented a change in the exchange rate regime—

resulted in the divergence of the official and unofficial exchanges rates, beginning in October 2014.

4.4 DOMESTIC ECONOMIC EVENTS AND BITCOIN EXCHANGE RATES

In Figure 5[b], the South African rand (ZAR) shows two clear episodes where bitcoin exchange

rates changed without any corresponding movement in the official exchange rate: on April 17,20January 2015 SNB press release (www.snb.ch/en/mmr/reference/pre 20150115/source/pre 20150115.en.pdf).

21

FIGURE 5Comparison of Bitcoin and Official Exchange Rates: High Barriers

(a) Mexican Peso (b) South African Rand

(c) Chinese Yuan (d) Argentinian Peso

2015, and on May 21, 2015. The timing of these bitcoin market deviations are linked to domestic

events that received only limited international attention—on April 17 there was mass anti-migrant

riots and violence, and on May 21 there were nationwide police raids, which resulted in approx-

imately 4000 arrests in connection to the riots the month before—suggestive evidence that the

bitcoin exchange rates are not formed purely by international speculators.

Turning to the Chinese yuan (CNY), Figure 5(c) shows that the official and bitcoin exchange

rates were slowly separating from each other. The eventual 1.9% exchange rate devaluation on

August 10, 2015, represents a noticeable trend break in both series, and has resulted in a bitcoin

and official Chinese exchange rate that is subsequently very similar in both trend and level (or more

22

succinctly, an official CNY rate that reflects the bitcoin market rate) implying that the devaluation

has succesfully realinged the Chinese and American currencies.

5 BITCOIN AND UNOFFICIAL EXCHANGE RATES

5.1 DETECTING EXCHANGE RATE REGIMES

While the most common officially reported exchange rate regime is a free- or managed-float

regime, Calvo and Reinhart [2002] found that the exchange rates of many countries resembled

that of a fixed or highly managed exchange rate (a phenomenon they termed “fear of floating”).

Crucially, Alesina and Wagner [2006] showed countries with relatively good institutions use a dec-

laration of a floating regime to signal their virtuousness, rather than countries with poor political

institutions (the typical suspects for bad or misreported data).

This inconsistency between the declared and actual exchange rate regimes has led to many at-

tempts to find other systems of classifying exchange rate regimes based not on self-reporting but

on observed behavior. Reinhart and Rogoff [2004] retroactively reclassified exchange rate regimes

using the observed behavior of the official and parallel exchange rate data between 1946 and 1998;

Levy-Yeyati and Sturzenegger [2005] constructed a classification based on official exchange rates

and international reserves; Shambaugh [2004] used the volatility of the official exchange rate;

while Quere, Coeure, and Mignon [2006] used a stability criteria against a market basket of cur-

rencies. Consequent to the findings of Calvo and Reinhart [2002], the IMF regime classification

now takes into consideration the behavior of the exchange rate in addition to the country’s official

statement.

Kiguel and O’Connell [1995] argued that a significant difference between the market and offi-

cial rates may signal fundamental macroeconomic misalignments; therefore, the difference should

be greater for managed exchange rates than it is for market exchange rates. I define the premium

23

between the official and bitcoin exchange rate, MCm,t , as:

MCm,t =

EB,Cm,t

EO,Ct−1 (10)

= (ρC +ρB +ρ

m−1)+εC,m

E0,Ct

(11)

Because there is a bitcoin-exchange-specific premium (given that the exchanges charge different

fees and have different structures), and Figure 2 showed that this premium was non-zero for some

exchanges even for the Euro, I adjust the premium by the value of the euro premium for the

exchange:

MCm,t = MC

m,t−MEURm,t (12)

I consider the mean of this adjusted premium to classify exchange rates. Note that is possible

for an exchange rate to have no barrier (ρ = 0), while still maintaining a positive premium εC.

This is consistent with exchange rate pegs maintained by domestic policy, instead of international

financial markets controls (which would have be detected using the methodology in Section 4.3).

5.2 EXCHANGE RATE REGIME

Table 4 lists the mean and standard deviation of the adjusted markup for each currency and bit-

coin exchange. Three clear clusters emerge: markups between 0 and 0.5%, which I categorize as

“Market” regimes; currencies with markups between 0.5 and 2%, which I categorize as “Mildly

Managed”; and the remainder categorized as “Highly Managed.” Within these three categories,

the currencies are sorted by the size of their markup. I compare these categories with the 2014

exchange rate regime identified by the IMF Annual Report on Exchange Arrangements and Ex-

change Restrictions, which is based on the behavior of the official exchange rate. The range of

the markup (as measured by the standard deviation) and the average markup both increase as the

exchange rate becomes increasingly managed.

24

TABLE 4Exchange Rate Regime and Markup

Currency Market Mean SD IMF Classification

Market (0.00%-0.50%)AUD ANX 0.04 0.49 Free floatCAD ANX 0.00 0.41 Free float

Local 0.14 4.51 Free floatGBP ANX -0.01 0.37 Free floatJPY ANX -0.00 0.43 Free floatNZD ANX 0.07 0.55 Float

Local 0.49 4.79 FloatSGD ANX 0.00 0.38 Stabilized arrangement

itBit -0.31 1.24 Stabilized arrangement

Mildly Managed (0.50%-2.00%)CNY ANX 0.72 0.81 Crawl-like arrangementNOK Local 0.74 4.66 Free floatSEK Local 1.21 4.31 Free floatMXN Local 1.11 4.90 Free floatCZK Local -1.55 8.20 Other managed arrangementRUB btce 1.91 3.95 Other managed arrangement

Highly Managed (2.00%+)PLN Local -4.89 5.56 Free floatTHB Local -4.36 4.45 FloatBRL Local 4.16 9.11 FloatZAR Local 6.21 9.67 FloatCHF ANX 7.19 12.01 Crawl-like arrangementARS Local 41.37 10.39 Crawl-like arrangementAbbreviations: ANX, ANXBTC; btce, BTC-e; Local, LocalBitcoin.

There are eight differences in classifications, with seven currencies found to be more managed

that their IMF classification suggests and one currency found to be less managed. The differences

are discussed in detail in Sections 5.2.1-5.2.3, and are similar to the reasons discussed in Section

4.3. Overall, once appropriately adjusted, bitcoin can be used to determined exchange rate regime.

5.2.1 Market Exchange Rate Regimes Bitcoin and the IMF disagree regarding the Singapore

dollar (SGD, Figure 3[e]), with the IMF considering it a stabilized arrangement and bitcoin clas-

sifying it as a floating exchange rate. I found low premiums on both bitcoin exchanges that sell

25

Singapore dollars. This result implies that while Singapore is officially managing its currency, the

resulting exchange rate is not substantially different from the market exchange rate.

5.2.2 Mildly Managed Exchange Rate Regimes The Norwegian krone (NOK) and the Swedish

krona (SEK) are both found to be more managed than recognized by the IMF, with obvious pre-

miums observable in Figures 4(c) and 4(k). These results may be a reflection of the political

and economic turbulence in the eurozone during this time. The issues surrounding the remaining

currency, the Mexican peso (MXN), were discussed in Section 4.3.

5.2.3 Highly Managed Exchange Rate Regimes The Polish zloty (PLN, Figure 4[a]) is classi-

fied by the IMF as a free float, but appears like a highly managed exchange rate when viewed by

bitcoin. Again, this discrepancy seems likely to be the effect of the eurozone crisis. The South

African rand (ZAR), a floating currency according to the IMF and a highly managed one accord-

ing to bitcoin, was discussed in Section 4.4. Both the Brazilian real (BRL) and Thai bhat (THB)

were found to be low barrier currencies: the IMF classifies them as floating, but they appear to

be highly managed exchange rate regimes based on the bitcoin premium. As detailed in Human

Rights Watch [2015], Thailand underwent a political coup by the military in May 2014, so the

premium may reflect underlying uncertainty regarding the economic stability of the country. A

similar explanation may also apply to Brazil, which faced a series of large protests in 2015 due

to alleged political corruption within the state owned energy company Petrobas, the beginning of

which is discussed in Prada [2015].

6 A COMPARISON OF OFFICIAL AND UNOFFICIAL EXCHANGE RATES

6.1 DO BITCOIN EXCHANGE RATES REFLECT UNOFFICIAL EXCHANGE RATES?

It seems reasonable, given that the bitcoin exchange rate is determined by the market, that it pro-

vides an estimate of a currency’s unofficial exchange rate, especially after controlling for bitcoin-

specific trends. Historically, unofficial exchange rate data have been both expensive and difficult to

26

obtain, and, because they are reported rather than directly observed the data are subject to quality

concerns. The ability to use the bitcoin exchange rate as a free alternative source for unofficial

exchange rate movement data could alleviate many of these concerns. The results in Section 4.1

(showing that there could be significant bitcoin and bitcoin exchange trends) should, however,

invite pause because it implies that bitcoin-specific trends may distort the bitcoin exchange rate.

To test whether bitcoin can be interpreted as the unofficial exchange rate, I examine the be-

havior of bitcoin relative to that of the unofficial Argentinian exchange rate. Argentina is widely

known to have a long-established crawling peg regime with the US dollar and a highly manipu-

lated exchange rate, and its unofficial exchange rate is reported daily by various sources (including

Argentinian newspapers), reducing many of the concerns typically associated with estimates of the

unofficial exchange rate.

FIGURE 6Comparison of Argentinian Exchange Rates

I obtain unofficial exchange rate data from Ambito Financiero, a daily newspaper based in

Buenos Aires. The official, unofficial, and adjusted bitcoin exchange rate of the Argentian Peso to

the US dollar are shown in Figure 6.21 A visual examination reveals that the bitcoin exchange rate

(dashed line) closely follows the time trend of the unofficial exchange rate (dotted line) but not the

21The bitcoin rate has been smoothed by a five-point smoothing filter to aid visual analysis.

27

official exchange rate (solid line).

Table 5 lists the corresponding cointegration test, VECM, and premium for the three exchange

rates. There is no cointegrating relationship between the official exchange rate and either the un-

official or bitcoin exchange rate, as expected given the strict capital controls. A cointegrating

relationship does exist for the unofficial and bitcoin exchange rates. Additionally, the VECM re-

veals that these two exchange rates obey the rLOP, reflecting the same information. These findings,

together with the earlier discussion of the South African rand (ZAR) exchange rate that showed

national domestic domestic events affecting the exchange rates suggests that bitcoin is not only

being used by speculative foreign investors but also by residents of these countries.

TABLE 5Relationship among Three Sources of Argentinian Exchange Rates

Official Official Unofficialand Unofficial and Bitcoin and Bitcoin

SBIC 3 6 3` 11 6 5

Cointegration TestJohansen: r = 0 4.24∗∗∗ 5.44∗∗∗ 39.48Johansen: r ≤ 1 1.22 0.79 0.54∗∗∗

Cointegrated? No No Yes

Barrierβ − − 0.79∗∗∗

ρ 1.00 1.00 0.05Low barrier? No No Yes

PremiumMean (%) 54.53 34.50 −12.91Adj. mean (%) 61.40 41.37 −6.04Abbreviations: SBIC, Schwarz Bayesian information criterion.***1%, ** 5%.

Interestingly, the data in Table 5 reveal that even though unofficial and bitcoin exchange rates

are cointegrated, there is a significant negative premium, even after adjusting the mean for the

bitcoin-specific markup (−6.04%). This persistence, even after adjusting for an exchange-specific

premium, must reflect an element that is not found in the bitcoin-based euro exchange rate and

therefore cannot be normalized. It could reflect, for example, the convenience and relative safety

28

of using bitcoin exchange rate channels that are not as relevant or significant for euro currency

transactions or similar floating-exchange-rate regimes. This indicates that bitcoin should not be

used to estimate the level-value of the unofficial exchange rate. However, given the cointegration

results bitcoin exchange rates can be used to determine trends of the unofficial exchange rate.

6.2 PROPORTIONALITY

The modeling approach of Dornbusch, Dantas, Pechman, Rocha, and Simoes [1983]—using a

portfolio choice model as the starting point for a model of dual exchange rate markets where

each exchange rate is the price of an asset (in this case, the currency)—is frequently used as a

launching point to examine the relationship between official and unofficial exchange rates. This

approach implies a long-run constant proportionality between the official and unofficial exchange

rates (or a rLOP between identical assets). Papers using multiyear datasets have found only mixed

evidence for a proportionality relationship: Caporale and Cerrate [2008] rejected a proportionality

relationship, while Bahmani-Oskoee, Miteza, and Nasir [2002] and Kula, Aslan, and Ozturk [2014]

found evidence in support of it.

TABLE 6Relationship of Exchange Rate Regime and Barriers to Foreign Exchange

BarriersExchange Rate Regime Low (11) Intermediate (3) High (4)

Market (6) AUD, CAD, GBP, − −JPY, NZD, SGD

Mildly managed (6) SEK, CZK, RUB NOK MXN, CNY

Highly managed (6) THB, BRL PLN, CHF ZAR, ARS

Table 6 summarizes the regime and exchange rate classification results for each currency. Re-

call that a finding of a low or intermediate barriers requires cointegration, so any low or inter-

mediate barrier result supports proportionality. Table 6 shows that all exchange rate regimes can

satisfy the proportionality requirement. Given that my barrier index broadly reflects the ordering

29

of KAOPEN, it implies that proportionality is more likely to be satisfied if countries do not im-

plement barriers and therefore, the mixed findings in the literature could reflect the existence of

unofficial barriers.

TABLE 7Causality Tests

Lag H0: O 6→ B H0: O 6← BCurrency Exchange SBIC ` Test Value P Value Test Value P Value Causality

Floating—Minimal barriersCAD ANX 1 2 4.63 0.10 3956.7 0.00 O↔ B

Local 2 2 14.67 0.00 0.82 0.66 O→ BAUD ANX 1 2 0.17 0.92 6102 0.00 O← BGBP ANX 1 3 4.74 0.19 3739.7 0.00 O← BJPY ANX 2 2 3.46 0.18 704.28 0.00 O← BNZD ANX 2 2 2.47 0.29 5297 0.00 O← BSGD ANX 2 2 1.70 0.43 2294.9 0.00 O← B

itBit 2 3 28.92 0.00 10.46 0.02 O↔ B

Mildly Managed—Minimal barriersCZK Local 2 5 11.71 0.04 1.93 0.86 O→ BSEK Local 2 2 7.58 0.02 2.02 0.37 O→ BRUB btce 2 2 4.54 0.10 99.87 0.00 O↔ B—Intermediate barriersNOK Local 2 3 11.81 0.01 14.22 0.00 O↔ B—High barriersMXN Local 2 2 6.31 0.04 10.16 0.01 O↔ BCNY ANX 2 4 1.81 0.77 128.6 0.00 O← B

Highly Managed—Minimal barriersTHB Local 2 2 2.08 0.35 15.44 0.00 O← BBRL Local 1 4 8.19 0.09 0.71 0.95 O→ B—Intermediate barriersPLN Local 2 3 8.27 0.04 0.12 0.99 O→ BCHF ANX 3 3 10.66 0.01 0.17 0.98 O→ B—High barriersZAR Local 2 6 14.61 0.02 11.85 0.07 O↔ BARS Local 6 6 4.81 0.57 4.69 0.58 O 6↔ BNote: x 6→ y stands for “x does not Granger-cause y.”Abbreviations: ANX, ANXBTC; btce, BTC-e; Local, LocalBitcoin.

30

6.3 CAUSALITY

The unofficial exchange rate is thought to Granger-cause the official exchange rate in a managed

exchange rate regime, as the unofficial exchange rate reflects current market information that may

take time to be reflected in the official rate. Baliamoune-Lutz and Lutz [2008] and Baliamoune-

Lutz [2010] documented that the black market exchange rate Granger-causes the official rates

Tunisia and Morocco (managed exchange rate regimes), providing support for this hypothesis.

However, Huett, Krapf, and Uysal [2014], found mutual causation between the official and unoffi-

cial exchange rates for the managed Belarusian ruble. Using the TY method described in Section

3.3.3, I test for Granger causality across all currencies. Unlike the aforementioned studies, I can

compare both floating and managed exchange rates, and currencies with and without binding bar-

riers to foreign exchange markets, over the same period and on a daily basis.

Table 7 presents the causality test results. There is no uniform pattern across barriers and ex-

change rate regimes. Half of the market regimes have causality from bitcoin to official exchange

rates, half of the mildly managed regimes have bidirectional causality, and half of the highly man-

aged regimes show causality from the official rate to bitcoin. A single direction of causality occurs

for 10 out of 13 currencies with low barriers, and for 1 out of 4 currencies with the highest level of

high barriers.

This result is not surprising if a change in the official exchange rate to an event that causes a

change in the unofficial exchange rate occurs only infrequently, and takes multiple days or weeks

to occur. This would weaken any causality relationship estimated on higher frequency daily data,

instead of monthly data. Indeed, Huett et al. [2014], who also did not find causality from unofficial

to official exchange rates, were also using daily data, lending support to this interpretation.

7 CONCLUSIONS

This work proposes a method to use bitcoin-transaction prices in various currencies to construct

a currency’s unofficial exchange rate, detect the size of barriers to the official exchange rate, and

31

identify exchange rate regimes. Bitcoin-based exchange rates can be used to identify episodes of

capital movement that, due to their transitory nature, current classification systems (such as the

IMF or the Chinn-Ito index) cannot detect. This method of identification has powerful implica-

tions for future applied and policy work, as bitcoin data are publicly available at no charge on a

daily basis—even as events unfold—and cannot be manipulated by bad reporting as could be the

case with the World Currency Yearbook or, to a lesser extent, the IMF classification system. Addi-

tionally, even if governments temporarily cease to gather data due to political or economic upset,

the bitcoin data continue to exist and accrue.

Findings from earlier work that show mixed evidence regarding Granger causality between

official and unofficial exchange rates is re-examined over the same time period for a variety of

regimes and barriers, and explained as causality is not found to consistently flow from the unoffi-

cial bitcoin rate to the official rate when using daily data. Even among highly managed regimes,

Granger causality exists in all variationsd. Proportionality between unofficial and official exchange

rates is possible for all regimes, but more likely to exist in the absence of barriers.

32

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